{"ID":6626576,"CreatedAt":"2026-07-15T02:56:36.47817413Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.12938","arxiv_id":"2607.12938","title":"Sharp Optimal Algorithm for Derivative-Free Stochastic Convex Optimization in One Dimension","abstract":"Stochastic convex optimization is a classical problem with well-understood guarantees under first-order feedback. In contrast, for zero-order optimization with noisy function evaluations, a logarithmic gap has persisted between known upper bounds and the $Ω(1/\\sqrt{T})$ lower bound, even in the one-dimensional case. In this work, we study the problem of minimizing a convex function $f : [0,1] \\to [0,1]$ using a zero-order oracle with subGaussian noise. We propose a computationally efficient algorithm that achieves the optimal $O(1/\\sqrt{T})$ convergence rate, matching the lower bound. The result closes the existing gap in one dimension, providing the first sharp rate guarantee in this setting.","short_abstract":"Stochastic convex optimization is a classical problem with well-understood guarantees under first-order feedback. In contrast, for zero-order optimization with noisy function evaluations, a logarithmic gap has persisted between known upper bounds and the $Ω(1/\\sqrt{T})$ lower bound, even in the one-dimensional case. In...","url_abs":"https://arxiv.org/abs/2607.12938","url_pdf":"https://arxiv.org/pdf/2607.12938v1","authors":"[\"Alexandra Carpentier\",\"Chloé Rouyer\",\"Alexandre Tsybakov\",\"Arya Akhavan\"]","published":"2026-07-14T16:10:33Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"stat.ML\"]","methods":"[]","has_code":false}